Most people consider these plants to be weeds and pull them out as soon as they are spotted in the garden. I happen to find them quite beautiful. Perhaps it is because as a child, they randomly grew throughout the wild areas in our big backyard. They are also fun because you can cut them and place them in a glass of colored water. After a few hours or a day, the white flower on the top will change to whatever color you have dyed the water. It's a great trick to use with young children to demonstrate how water travels from the roots, up the stem, to the flower.
These white weeds resemble the perennial plant yarrow. My father loved to have yarrow in his yard. It made my mom crazy because she always thought it was Queen Anne's Lace and wanted to pull them out. She grew up on a farm and spent many hours having to weed along the tomato plants. I have a tendency to allow them to stay - within reason.